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  • Mean Kinetic Energy
  • Mean Kinetic Energy
  • Kinetic Energy Loss
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  • Total Kinetic Energy
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Articles published on Kinetic energy

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  • New
  • Research Article
  • 10.1063/5.0338300
Isomerization dynamics of dicationic CS2 and OCS driven by electron-impact.
  • Jul 7, 2026
  • The Journal of chemical physics
  • Wenguang Wu + 6 more

The isomerization of dications of CS2 and OCS is investigated using combined experimental and theoretical methods. The dications were generated by a high-energy electron pulse and the fragment ions were detected by a momentum imaging time-of-flight spectrometer. Bond rearrangement reactions leading to C+ + S2+ and C+ + OS+ were identified through coincident measurements. Theoretically, potential energy surfaces along the reaction paths were calculated using high-level quantum chemistry methods. For CS2+, isomerization is initiated by ionization excitation followed by a decay process. In contrast, the isomerization channel for OCS2+ can open on the ground dicationic state through vibrational excitation. The predicted kinetic energy releases agree with the experimental data. This study demonstrates that, as a common process in dissociative ionization, isomerization mechanism may be influenced by molecular symmetry.

  • New
  • Research Article
  • 10.1016/j.jbiomech.2026.113378
Sensitivity of brain injury criteria to anthropometric scaling assumptions in instrumented mouthguard data.
  • Jul 1, 2026
  • Journal of biomechanics
  • Melanie Dawn Bussey + 2 more

Sensitivity of brain injury criteria to anthropometric scaling assumptions in instrumented mouthguard data.

  • New
  • Research Article
  • 10.1016/j.gsf.2026.102297
Physics-informed synergy regional co-seismic landslide size prediction: A novel data-driven approach for improved reliability and interpretability
  • Jul 1, 2026
  • Geoscience Frontiers
  • Binghai Gao + 5 more

Physics-informed synergy regional co-seismic landslide size prediction: A novel data-driven approach for improved reliability and interpretability

  • New
  • Research Article
  • 10.1007/s10439-026-04037-5
In-Vivo 6D Heart Motion Analysis for Emerging Self-Powered Cardiac Implants.
  • Jul 1, 2026
  • Annals of biomedical engineering
  • Milad Hasani + 5 more

Self-powered intracardiac implant devices show great promise for future clinical applications due to their extended operational lifespan and the potential to reduce the need for high-risk repeat surgeries. This study investigates the feasibility of harvesting energy from cardiac motion through in vivo testing of intracardiac devices. Comprehensive three-dimensional translational and rotational cardiac motions are captured in a porcine model using a miniaturized 9-degree-of-freedom motion sensor implanted at six strategic epicardial sites. Kinematic criteria are developed to evaluate the energy harvesting potential of each implant site based on the available kinetic energy, acceleration, and jerk factors. The recorded heart motion signals are analyzed and applied to a conceptual energy harvester proposed to identify the optimal implant site. The results reveal that the left ventricular apex emerges as a preferable site for energy harvesting, particularly at moderate heart rates. These findings offer valuable insights into optimizing self-powered intracardiac implants, reducing dependency on battery replacements, and enhancing long-term patient safety.

  • New
  • Research Article
  • 10.1039/d6cp00651e
Interstellar ice embedded glycine response to H+/proton irradiation. A theoretical study.
  • Jul 1, 2026
  • Physical chemistry chemical physics : PCCP
  • Maysa Yusef-Buey + 3 more

The glycine molecule is the simplest amino acid molecule which is expected to be easily formed on ice grains in the interstellar medium. Assessing its stability under interstellar irradiation is therefore crucial in a prebiotic context. In this work we investigate the ionisation mechanism of ice-embedded glycine under H+ irradiation at kinetic energies of 1, 10, and 100 keV by studying charge and energy deposition dynamics. To this aim, real time-time dependent-density functional theory combined with a quantum mechanics/molecular mechanics approach is used. Charge distribution analysis reveals ebb-and-flow effects at both molecular and atomic scales, with collisions at nuclei inducing stronger polarization and dipole dynamics than impacts along chemical bonds. While electronic excitation occurs locally, glycine-water interactions can collectively enhance, reduce or leave unchanged the energy deposition, depending on the projectile trajectory and kinetic energy. The charge transfer between the glycine molecule and its surrounding environment does not exceed 0.4 electrons once the projectile is gone. When the projectile does not directly intersect the glycine backbone, the deposited energy on the glycine molecule is negligible and glycine remains neutral. Consequently, the degree of molecular perturbation is governed not only by the projectile's energy, but also by its microscopic trajectory and the surrounding ice environment.

  • New
  • Research Article
  • 10.1002/mrm.70317
FlowVN Trained on a Single Dataset Enables Rapid Reconstruction of Highly Accelerated 4D Flow MRI Across Multiple Sites.
  • Jul 1, 2026
  • Magnetic resonance in medicine
  • Sohaib Ayaz Qazi + 6 more

The aim of this study is to evaluate a deep variational network, FlowVN, for the reconstruction of heavily undersampled 4D Flow MRI across multiple sites. FlowVN was trained on fully sampled 4D Flow MRI datasets of healthy volunteers from one site. The model was tested on retrospective undersampled data (R = 6-22) of six normal volunteers from the same site and six from another site, prospectively undersampled data (R = 12.4-13.8) of six healthy volunteers from the second site and six patients with aortic stenosis from first Site. Performance was evaluated using nRMSE, relative and angular error, average and maximum velocity, flow rate, volumetric flow, and turbulent kinetic energy (TKE), with a Wilcoxon signed-rank test to assess the difference from ground truth. FlowVN showed minimal sensitivity to the number of training datasets and performed well even when trained on a single dataset. FlowVN also demonstrated good generalizability across sites. No significant difference in average and maximum velocity was observed up to R = 16. Total TKE was preserved up to R = 10 in the normal volunteers, but was well preserved even at higher acceleration factors in the aortic stenosis patients. Flow volumes through the ascending and descending aorta were well preserved for all acceleration factors, although ascending aorta flow volumes for data from one site were significantly different from ground truth for AF > 16. FlowVN accurately reconstructs highly undersampled 4D Flow MRI from multiple sites using a model trained on a single dataset, maintaining excellent quantitative image quality even at very high acceleration factors.

  • New
  • Research Article
  • 10.1016/j.triboint.2026.111826
Friction torque of deep groove ball bearing with grease-lubricated based on kinetic energy deceleration method
  • Jul 1, 2026
  • Tribology International
  • Panlong Wu + 8 more

Friction torque of deep groove ball bearing with grease-lubricated based on kinetic energy deceleration method

  • New
  • Research Article
  • 10.1016/j.jfluidstructs.2026.104560
Self-adaptive elastic flaps with bending and torsion for 3D blunt body drag reduction
  • Jul 1, 2026
  • Journal of Fluids and Structures
  • J.M Camacho-Sánchez + 4 more

Self-adaptive elastic flaps with bending and torsion for 3D blunt body drag reduction

  • New
  • Research Article
  • 10.1021/acs.jpca.6c02947
Photodissociation Dynamics of the Zn+(Acetylene) and Zn+(Ethylene) Cation-π Complexes.
  • Jun 30, 2026
  • The journal of physical chemistry. A
  • John R C Blais + 2 more

Zn+(acetylene) and Zn+(ethylene) ion-molecule complexes are investigated in the gas phase with selected-ion photofragment imaging. UV photodissociation produces respectively Zn+ and C2H2+ or Zn+ and C2H4+ fragment channels, revealing both simple bond cleavage and charge-transfer dissociation in these complexes. Imaging of each fragment channel reveals considerable kinetic energy release (KER), which provides upper limits on the bond dissociation energies (BDEs): D0 ≤ 1.04 ± 0.20 eV (24.0 ± 4.6 kcal/mol) for Zn+-(C2H2) and D0 ≤ 0.82 ± 0.18 eV (18.9 ± 4.2 kcal/mol) for Zn+-(C2H4). Agreement with previous data from spectroscopic measurements on Zn+(C2H4) suggest that these upper limits are near the true BDE for each of these complexes. Density functional theory (DFT) calculations explore the bonding and structures of the Zn+(C2H2) and Zn+(C2H4) ions, employing the B3LYP, M06, M06-L, and MN15-L functionals. Time-dependent DFT (TD-DFT) computations at the B3LYP/def2-QZVP level characterize the excited states of these complexes. Zn+(C2H2) dissociates via absorption to the bound 2B2 excited state followed by curve crossing to the 2A1 charge-transfer excited state, whereas Zn+(C2H4) dissociates via direct excitation of the charge-transfer state.

  • New
  • Research Article
  • 10.1021/acs.langmuir.6c02917
Asymmetric Interfacial Dynamics during Oblique Impact of Two Unequal-Sized Nanodroplets on Superhydrophobic Surfaces.
  • Jun 30, 2026
  • Langmuir : the ACS journal of surfaces and colloids
  • Mingjun Liao + 4 more

Molecular-level understanding of droplet rebound on nonwetting surfaces is important for controlling liquid transport and removal. In this work, molecular dynamics simulations are used to investigate the oblique impact of two unequal-sized nanodroplets on a superhydrophobic Pt surface. The effects of Weber number and inclination angle on impact morphology, spreading, rebound, and energy dissipation are systematically examined. With increasing Weber number, the impact outcome evolves from regular deposition to regular bouncing, hole bouncing, and breakup-dominated states. Increasing the inclination angle enhances tangential momentum and impact asymmetry, thereby promoting perforation and fragmentation while reducing the maximum spreading factor. An inclination-corrected scaling relation, We0.382Re0.411 sinα-0.365, better describes the spreading behavior than conventional inclination-independent correlations. Rebound analysis shows that the inclination angle regulates horizontal displacement, restitution coefficient, takeoff velocity, and contact time by altering momentum partition and asymmetric recoil. Energy analysis further indicates that although viscous dissipation increases with Weber number, its proportion relative to the initial kinetic energy decreases. More importantly, the coupling between oblique impact and droplet-size asymmetry activates a rolling-assisted rebound mode, providing an additional route for energy redistribution. These results reveal how dynamic and geometric asymmetries govern nanodroplet mobility on superhydrophobic surfaces.

  • New
  • Research Article
  • 10.1021/acsnano.6c06727
Nonadiabatic Dynamics of Photoinduced Hydrogen Dissociation on Plasmonic Au Nanoparticles: How Hot Carrier Excitation Leads to Bond Breaking.
  • Jun 29, 2026
  • ACS nano
  • Moumita Kar + 1 more

Plasmonic nanoparticles have generated great attention due to their potential applications in photocatalysis. The dissociation of hydrogen on Au nanoparticles has served as a useful model for this process, but despite many previous studies, there are important details of the dynamics which remain uncertain, such how single-photon absorption triggers dissociation. This paper addresses these issues through the study of gold clusters interacting with H2, explicitly examining the effects of cluster size, shape, and excitation energy on the dissociation dynamics. By using time-dependent density functional theory (TDDFT) interfaced with trajectory surface hopping, we have examined the Au + H2 system for states with excitation energies similar to the plasmon energy in gold. Three distinct outcomes are observed: H-H bond dissociation, H2 desorption, and nonreactive relaxation. Trajectories starting in excited states of the cluster relax through extensive nonadiabatic surface hopping to lower excited states that couple to antibonding states where repulsion drives dissociation. In addition, hopping converts metal excitation to increased kinetic energy in H-H stretching that helps overcome dissociation barriers on reactive adiabats. This provides a detailed picture of the evolution of hot carriers into antibonding states of physisorbed molecules after extensive surface hopping that dissociate in ∼100 fs. Desorption and nonreactive relaxation compete with this picture. Our findings provide insights to photoinduced processes involving plasmonic nanoparticles showing how nonadiabatic dynamics plays a crucial role in accessing repulsive states while also releasing kinetic energy that drives dissociation.

  • New
  • Research Article
  • 10.1038/s41598-026-59177-4
Dynamics of water droplet tumble over obstacles on hydrophobic surfaces.
  • Jun 29, 2026
  • Scientific reports
  • Bekir Sami Yilbas + 6 more

Dust accumulation and wind effects can form structure-like obstacles on exposed surfaces, making it challenging to remove dust using rolling water droplets, as the droplets encounter obstacles of varying sizes during their motion. Controlling droplet motion over dusty surfaces becomes vital for efficient self-cleaning process. In this study, droplet motions including rolling, wobbling, tumbling over obstacles, and breaking off are investigated through a scaling-based estimate rather than a general predictive framework for all possible droplet-obstacle interactions. Numerical simulations and experimental observations are also provided within frame of parameters incorporated. Hydrophobic sample surfaces were created by dip-coating with functionalized nanoscale silica particles, which in turn results in a wetting state characterized by a contact angle of ~ 152.1° ± 0.9°, contact angle hysteresis of ~ 1.5° ± 0.9°, and a roughness parameter of ~ 1.62. The rolling droplet exhibits wobbling, and its dynamic motion alters both the mass center and contact angle hysteresis of droplet incorporated in the present study. This variation modifies the griping and interfacial friction forces acting on the droplet, effects that become more pronounced for larger droplets. The experimental conditions were designed to illustrate both tumbling and non-tumbling behavior of droplets as they rolled over obstacles. The inherited spin of the droplet has minimal influence on the jump length and contact time of droplet on hydrophobic surface. Droplets undergo break off for relatively large inertia (Weber number [Formula: see text] 10), which becomes more pronounced when the obstacle height exceeds one-quarter of the droplet diameter; however, the proposed breakup criterion and newborn-droplet size estimate are valid within the tested range of droplet volumes, obstacle geometries, inclination angles, and surface properties considered in the present study. The radius of the newborn droplets varies inversely with Weber number such that [Formula: see text] for the cases considered in the present study. The newborn droplets reduce droplet kinetic energy by an amount of [Formula: see text] while influencing the oblique impact dynamics of the tumbled droplet within the investigated parameters range. Although the present study provides useful information on droplet tumble characteristics and breakoff in relation to self-cleaning applications, we acknowledge that the number of newborn droplets, the detailed breakup morphology, and the transferability of the results to other surface chemistries or real outdoor dusty environments remain outside the fully validated scope of the present work.

  • New
  • Research Article
  • 10.1021/acs.langmuir.6c02548
Regulation of Coalescence-Induced Droplet Jumping by Triangular Protrusions on Superhydrophobic Surfaces.
  • Jun 29, 2026
  • Langmuir : the ACS journal of surfaces and colloids
  • Xiaoyu Wang + 2 more

Coalescence-induced droplet jumping provides a passive, spontaneous route to enhance condensation heat transfer, anti-icing, self-cleaning, and atmospheric water harvesting. However, conventional superhydrophobic surfaces are severely constrained by low energy conversion efficiency and uncontrolled jumping directions. Here, we fabricate a monolithic superhydrophobic surface featuring triangular protrusions via 3D printing and systematically investigate the effects of protrusion height (450-900 μm), apex angle (30°-150°), and droplet radius (0.75-1.20 mm) on coalescence-induced jumping dynamics using high-speed imaging. Compared with flat superhydrophobic surfaces, the triangular-protrusion architecture substantially enhances jumping height, dimensionless jumping velocity, and projected directional deflection of the merged droplets. Notably, the energy conversion efficiency, defined here as the experimentally accessible translational energy conversion fraction ηt, is increased by approximately 827% compared with that on the flat superhydrophobic surface. Parametric analyses reveal that taller protrusions promote directional jumping by suppressing nontarget lateral spreading. The apex-angle dependence exhibits a pronounced nonmonotonic trend, with the 60° geometry delivering optimal performance by balancing directional spreading capability and recoil recovery. Velocity-component decomposition demonstrates that the protrusions regulate droplet jumping primarily by redistributing horizontal and vertical velocity components at detachment. This work establishes a simple macroscopic geometric strategy that increases the experimentally accessible translational energy conversion fraction and improves the projected directional regulation of coalescence-induced droplet jumping, thereby offering design principles for next-generation functional interfaces.

  • New
  • Research Article
  • 10.1021/acs.est.6c05455
Turning Motion into Methane: Electromagnetic Induction in Microbial Aggregates Enhances Wastewater Resource Recovery.
  • Jun 28, 2026
  • Environmental science & technology
  • Pengyu Chen + 15 more

Microbial aggregates in wastewater treatment systems generate substantial kinetic energy through their motion, which constitutes ubiquitous but untapped energy. Here, we demonstrate that this kinetic energy can be harvested and converted into bioavailable electrochemical potential to drive the microbial metabolism. In anaerobic reactors, aggregates moving perpendicular to a designed magnetic field generate an in situ electrical potential via electromagnetic induction through their conductive pili networks, thereby enabling the direct conversion of microbial motion into methane via metabolic energy capture. Integrated multi-omics, microbial community, and electrochemical analyses showed that the continuous conductive network formed between electroactive microorganisms and methanogens via e-pili was key to the conversion of kinetic energy into electrical potential through electromagnetic processes. The induced potential not only enhanced the electrochemical activity and conductivity of microbial aggregates but also stimulated respiratory electron transfer in electroactive microorganisms and activated energy-conserving electron bifurcation in methanogens. Energy, economic, and carbon footprint analyses showed that kinetic energy recovery increased net energy recovery by 226%, reduced greenhouse gas emissions by 25%, and improved economic returns. Our work establishes a direct pathway to convert microbial motion into biochemical energy, advancing sustainable resource recovery from wastewater.

  • New
  • Research Article
  • 10.1063/5.0331209
Modeling the coincident three-ion momentum imaging of diiodomethane photodissociation on reduced-dimensional potential energy surfaces.
  • Jun 28, 2026
  • The Journal of chemical physics
  • Yijue Ding

We present an efficient theoretical model to simulate observables in the time-resolved coincident three-ion Coulomb explosion experiment of diiodomethane. The model employs two degrees of freedom to describe the C-I bond breaking and the CH2I rotation during photodissociation and three degrees of freedom to describe the coincident CH2++I2++I2+ fragmentation during the subsequent Coulomb explosion. By solving the equations of motion, the photodissociation pathways are obtained on two-dimensional potential energy surfaces of the valence excited states of the neutral molecule, and the asymptotic momenta of the three ionic fragments are determined on the three-dimensional ground-state potential energy surface of the fivefold-charged cation. The photodissociation pathways are consistent with previous abinitio molecular dynamics simulations and indicate a CH2I rotational period of ∼340fs. The theoretical time-resolved kinetic energy release and the correlation between the kinetic energy release and the angle between the two I2+ momenta show good agreement with experimental signals in part, reflecting and confirming the static CH2I2 state and the CH2I + I dissociation channels.

  • New
  • Research Article
  • 10.1080/00084433.2026.2684194
Research on interpretable prediction of blast furnace hearth activity based on ensemble model
  • Jun 27, 2026
  • Canadian Metallurgical Quarterly
  • Li Hong-Yang + 4 more

ABSTRACT To address the strong lag and one-sided single-parameter characterisation issues in existing blast furnace hearth activity evaluation indicators, this paper proposes a multi-parameter fusion-based hearth activity index (LI) and an interpretable prediction model. Thirty-four operating parameters in six categories including raw materials, pressure, and temperature are selected as basic data. The entropy weight method is used to objectively weight the tuyere raceway comprehensive index (HAI), dead man temperature (DMT), and dead man cleanliness index (DCI) to construct the comprehensive index LI. A Bayesian Optimization (BO)-optimised LGBM-XGBoost Stacking ensemble model is established, with 5-fold cross-validation to improve generalisation ability. The SHAP method is adopted to analyse the influence mechanism of feature parameters. Verification using actual production data shows excellent prediction performance. SHAP analysis identifies blast kinetic energy, theoretical combustion temperature, and oxygen enrichment rate as core influencing factors. This study provides a new approach for real-time monitoring and precise regulation of blast furnace hearth activity.

  • New
  • Research Article
  • 10.1038/s41598-026-60080-1
Insights into the formation mechanism and motion dynamics of the Hongtupo Landslide, Wudu District, China.
  • Jun 27, 2026
  • Scientific reports
  • Miaomiao Li + 4 more

The Hongtupo landslide in Wudu District, Longnan City, triggered by the 1879 Wudu earthquake, posed a severe threat to human life and property. To investigate its formation mechanism, kinematic characteristics, and dynamic evolution, field investigations, geological background analyses, and numerical modeling were conducted. A two-dimensional discrete element model was established and calibrated using biaxial numerical tests to reproduce the complete landslide movement. The simulation results show that the landslide lasted approximately 120 s, with a maximum velocity of 25 m/s and a runout distance of 561 m. Energy evolution during the runout process was dominated by frictional dissipation, collisional energy dissipation, and kinetic energy transformation. The dynamic process of the landslide can be divided into four stages: initiation (0-15 s), acceleration (15-70 s), deceleration (70-110 s), and stabilization (110-120 s). During the movement, the velocity at the top was higher than at the bottom, and the surface velocity exceeded the internal velocity, indicating a thrust-driven sliding mechanism. The simulated topography is generally consistent with field observations, providing important reference for the prevention and mitigation of landslide-related geological hazards in the region.

  • New
  • Research Article
  • 10.1021/acs.jpcb.6c00759
Thermodynamic and Vapor-Liquid Equilibrium Properties of Deuterium from an Ab Initio-Based Intermolecular Potential.
  • Jun 25, 2026
  • The journal of physical chemistry. B
  • Ulrich K Deiters + 1 more

Molecular simulation with an ab initio-based intermolecular potential is used to investigate the atomic-level interactions responsible for the thermodynamic properties and vapor-liquid-equilibria (VLE) of deuterium (D2). Results are reported for pressures up to 100 MPa at both low (cryogenic) and ambient temperatures. The combination of a simplified ab initio atomic potential (SAAP) with Feynman-Hibbs first order (FH1) interactions closely reproduces the VLE phase envelope over a wide range of densities, resulting in good estimates of the critical properties. It also accurately reproduces the behavior of the second virial coefficient and pressure-temperature-volume properties. The analysis indicates that deuterium and hydrogen share the same intermolecular potential, i.e., SAAP(H2) + FH1. Additional quantum corrections to the kinetic energy (QCKE) are used to determine the enthalpy, heat capacities, isochoric pressure coefficient, isobaric thermal expansion coefficient, Joule-Thomson coefficient and the speed of sound. At cryogenic conditions, using QCKE yields close agreement with reference values for these properties.

  • New
  • Research Article
  • 10.1021/acsomega.5c10261
Interface and Thermophysical Properties of R32 Refrigerant.
  • Jun 23, 2026
  • ACS omega
  • Abibat Adekoya-Olowofela + 2 more

Driven by the urgent demand for efficient cooling in microelectronics and advanced thermal management systems, difluoromethane (R32/CH2F2) has emerged as a promising candidate owing to its favorable thermophysical properties, including high heat transfer efficiency and low viscosity. While bulk properties such as density, viscosity, and thermal conductivity have been widely studied, interfacial properties, including surface tension and interfacial thickness, remain comparatively underexplored, despite their importance in phase-transition dynamics. Here, we perform molecular dynamics (MD) simulations from 180 to 300 K using an optimized transferable force field for fluoropropenes with enhanced electrostatics to assess both bulk and interfacial behavior of R32. Simulations reproduced density within ±2.1%, viscosity within 3.05%, and thermal conductivity within 7.41% of NIST reference data. Heat capacities (C p and C v) were predicted within 5%. For interfacial properties, surface tension trends were reproduced within 13.58% deviation, and the vapor-liquid coexistence curve closely matched reference data, yielding a critical temperature of 345.7 K (1.6% deviation) and a critical density of 0.397 g/cm3 (6.4% deviation). Importantly, the vapor-liquid interface exhibited pronounced temperature-dependent broadening across the 180-290 K range. This behavior correlates with increasing molecular kinetic energy, reduction in intermolecular cohesive interactions, and a progressive loss of preferential dipole alignment, which collectively enhance thermal fluctuation amplitudes at elevated temperatures. These validated results provide predictive molecular-level insights, particularly for interfacial properties that remain less characterized. By reducing property prediction errors in key parameters such as critical temperature, this work provides reliable inputs for heat-exchanger and system models. Such correlations can support optimized component sizing, improved performance, and reduced refrigerant charge. Beyond R32, the methodology offers a transferable framework for blended and next-generation low-GWP refrigerants, contributing to sustainable thermal management aligned with the 2027 EU F-Gas regulation and 2030 Kigali Amendment.

  • New
  • Research Article
  • 10.1021/acs.jctc.6c00305
Spin-Orbit-Induced Nonadiabatic Dynamics: An Exact Ω Representation.
  • Jun 23, 2026
  • Journal of chemical theory and computation
  • Ryan P Brady + 1 more

Transforming rovibronic Hamiltonians of molecular systems from the ΛS (Hund's case a) basis to the adiabatic Ω representation is widely used to "remove" spin-orbit coupling (SOC) and enable single-state treatments of spectra and dynamics. We show that this simplification is only apparent: the SOC elimination necessarily generates sizable nonadiabatic couplings (NACs) from the nuclear kinetic energy operator. Neglecting these spin-orbit-induced NACs causes severe errors in rovibronic energies and transition properties. Using an analytically tractable two electronic-state model and high-accuracy variational benchmarks, we derive the exact conditions for numerical equivalence between Ω and ΛS formulations and quantify how missing NAC terms and bond-length-dependent spin factors degrade predictions. We implement a complete Ω-representation workflow in Duo for diatomics, fully transforming all Hamiltonian terms and enabling side-by-side Ω versus ΛS calculations. For common single-state pipelines (e.g., LEVEL), we provide diagnostics that flag unsafe regimes and practical remedies to restore accuracy. The results deliver actionable guidance for spectroscopy, photophysics, and kinetics: Ω-based single-state approximations are reliable only when interacting states are well separated in the Franck-Condon region; otherwise, explicit nonadiabatic terms are required─even for "forbidden" transitions.

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